work.cpp

0.618法和费波南希发的程序设计

#include<iostream>
#include<cmath>
using namespace std;
double f(double x)     
{
 return x*x+exp(-1.0*x);
}
int fibonacci(int n)       // 求解Fibonacci数列
{
 if(n==0||n==1)  return 1;
 else return fibonacci(n-1)+fibonacci(n-2);
}
void f_fibonacci(double a,double b,double x,double y,double l)  //fibonacci法
{
   int n=1;               //计算迭代次数
   while(fibonacci(n)<=(b-a)/l)     
   {
      n++;
   }
  for(int k=1;k<=n-2;k++)
  {
    x=a+(b-a)*fibonacci(n-k-1)/fibonacci(n-k+1);
    y=a+(b-a)*fibonacci(n-k)/fibonacci(n-k+1);
    cout<<"迭代次数:"<<k<<"  "<<"试探点为:"<<x<<"  "<<y<<"  "<<"函数值分别为:"<<f(x)<<"  "<<f(y)<<endl;
    if(f(x) >f(y))  a=x;
    else b=y;
  }
  double m;            //判别常数
  cout<<"输入辨别常数:";
  cin>>m;
  y=x+m;             
  if(f(x)>f(y)) a=x;
  else b=x;
  cout<<"极小点:"<<(a+b)/2<<"  "<<"函数值:"<<f((a+b)/2)<<endl;
}
void f_f2(double a,double b,double x,double y,double l)   //0.168法
{
 for(int k=1;;k++)
  {
    x=a+0.382*(b-a);
    y=a+0.618*(b-a);
    cout<<"迭代次数:"<<k<<"  "<<"试探点为:"<<x<<"  "<<y<<"  "<<"函数值分别为:"<<f(x)<<"  "<<f(y)<<endl;
    if(f(x) >f(y))  a=x;
    else b=y;
    if((b-a) <l) break;
  }
cout<<"极小点:"<<(a+b)/2<<"  "<<"函数值:"<<f((a+b)/2)<<endl;
}
void main()
{
 double a,b,l;          //初始区间[a,b]，精度l
 cout<<"输入初始区间：";
 cin>>a>>b;
 cout<<"输入精度:";
 cin>>l;
 double x,y;            //试探点x,y
 /*int c;
 cout<<"若选择用fibonacci法输入1，选用0.618法输入2：";
 cin>>c;
 switch(c)
 {
   case 1: f_fibonacci(a,b,x,y,l);
	       break;
   case 2: f_f2(a,b,x,y,l);
	       break;
   default: cout<<"error input"; 
 }*/
 cout<<"0.618法的结果如下:\n";
 f_f2(a,b,x,y,l);
 cout<<"fibonacci法的结果如下:\n";
 f_fibonacci(a,b,x,y,l);
 
}